When an equilateral prism is in the minimum deviation the angle of incidence is?

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Find the angle of minimum deviation for an equilateral prism made of a material of refractive index 1.732. What is the angle of incidence for this deviation?

Given,
Refractive index (μ) of the material from which prism is made = 1.732We know refractive index is given by:\[\mu = \frac{\sin\left[ \frac{\delta_\min + A}{2} \right]}{\sin\left[ \frac{A}{2} \right]}\]

Where δmin is the angle of minimum deviation and A is the angle of prism = 60˚\[\Rightarrow 1 . 732 \times \sin (30^\circ ) = \sin \left( \frac{\delta_\min + 60^\circ }{2} \right)\]\[\Rightarrow \frac{1 . 732}{2} = \sin \left( \frac{\delta_\min + 60^\circ }{2} \right)\]\[\Rightarrow \left( \frac{\delta_\min + 60^\circ }{2} \right) = 60^\circ\]

δmin = 60°

δmin = 2i − A
2i = 120°
i = 60°
Hence, the required angle of deviation is 60°.

Concept: Refraction Through a Prism

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